Eliminating φ from η equations

Approximating φ to a given order and specified mode

This is the equation that needs to be solved for : η'= + α

phiEquation expands the right hand side of the phi equation to order N and mode M. The highest order alpha term in the double sum will always be dropped, so the sum only goes to .

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This turns off the right hand side pattern warning message. The reason this defination of phi works is because phiEqn contains the lower orders of phi, which are immidiately evaluated. φ is programs to save calculated orders, so one it figures an order out, it plugs it in everywhere, and the solver works.

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φt is a total order sum for a given mode

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Plugging in for Phi into η equations

We are trying to eliminate φ from the following equations. Mathematica seems to be finicky (or I haven't figured out an alternative) with taylor series O notation; this needs to be figured out.

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Created by Mathematica (June 26, 2006) |